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By Igor Zh. Bunim, Valentine A. Chanturiya, Alexey T. Kovalev, Irina A. Khabarova, Elizaveta V. Koporulina

This paper presents new theoretical and experimental data on possible mechanisms for the formation of micro- and nanophases on the surface of sulfide minerals un der the effect of high-power nanosecond electromagnetic pulses (HPEMP). The gas outflow from nanosecond breakdown channels of sulfide minerals under the effect of HPEMP is considered, with allowance for the condensation of iron vapors. The condensation of matter in an outflowing jet is shown to be an effective mechanism for structureal and chemical transformations of sulfide surfaces. It is established that electrode potential of pyrrhotite is moved together in the negative party owing to formation of iron oxides (hydroxides) and iron sulfates by HPEMP, that provides decrease of xanthate sorption and reduction flotation extraction of this sulfide, whereas electrode potential of pentlandite gets more positive values at the expense of additional formation of element sulfur, that causes increase of xanthate sorption and, as a consequence, increase of nickel sulfide extraction.

Jan 1, 2012

By Y. C. Avniel, T. E. Warner

"It is important to be able to measure sulphur and nitrogen in molten iron and steel on-line. Unfortunately, there are no solid electrolytes which are stable under oxidising conditions and in which the ions of these species are mobile. In this paper, novel applications of beta alumina electrolytes are described and the results compared with data in the literature. Excellent agreement was obtained confirming this approach as a viable method of detecting elements whose ions are not mobile in solid electrolytes.IntroductionIn the past two decades, the rate of many processes in steelmaking have increased substantially. The sophistication of chemical analysis has also increased but analytical equipment is frequently positioned a significant distance from the operating plant which dictates that time is spent taking a sample, sending it to the analytical facility, preparation of the analytical sample prior to insertion into the equipment. In many cases, the time taken for analysis can exceed the time taken for the actual process and is now the rate defining step. Furthermore, most analytical methods are unable to distinguish between the amount of element which is dissolved in the steel and that contained in precipitates. Even if the analytical equipment could separate these two, the distribution would have changed between the molten steel and the cast sample. It would be an advantage to analyse on-line for impurities in molten metals."

Jan 1, 1997

By Takahiro Miki

Soldering material widely used is Sn-Pb alloy, which have low melting point and excellent electrical, strength properties and wettability. However, Pb is one of the toxic elements, which is undesirable due to environmental and safety reasons, thus Pb-free alternative alloy is preferred for new soldering material. Sn-Ag and Sn-Zn based alloys have been viewed as very promising candidates, among many potential substitutes. Addition of third element to these alloys will decrease melting point of the alloys. Hence, Sn-Ag-In and Sn-Zn-Mg alloys are expected to be suitable for replacing Sn-Pb solder alloy. In order to design new Pb-free soldering materials, it is crucial to understand precise thermodynamic properties and phase diagrams of alloy systems. In the present work, ion current ratios of Ag to In and Mg to Zn were measured for Sn-Ag-In and Sn-Zn-Mg alloys by mass spectrometry, respectively. Also, the authors reviewed the thermodynamic properties of terminal binary alloys determined by other researchers and evaluated a thermodynamic functions to express the excess Gibbs free energy of each binary alloy. Thermodynamic functions to express the excess Gibbs free energy of liquid Sn-Ag-In and Sn-Zn-Mg ternary alloys were determined, utilizing the assessed Gibbs free energy of terminal binary alloys with the measured ion current ratios using mass spectrometer.

Jan 1, 2003

By Mikiya Tanaka, Mikio Kobayashi, Kazuya Koyama, Yoshihiro Nishisu

Preparation of multicomponent powders are very useful and important for producing the materials with complicated and homogeneous structure. Therefore multicomponent powders have a lot of attention in the field of advanced value-added materials. The aqueous processing in hydrometallurgy has a broad potential for producing multicomponent homogeneous precipitates. Furthermore the aqueous processing has a future potential for integrating the separation, precipitation and synthesis processes. In this presentation the precipitation from homogeneous solution including rare-earths and/or common metals is presented. These precipitates probably consist of almost monodispersed, multicomponent and spherical particles by precisely controlling several reaction factors, reaction temperature, concentrations of starting materials, pH and so on. The separation of the nucleation stage and the growth stage of the particles is very important and how to control the reaction factors to realize enough separation is discussed. In this presentation the systems of Y-Eu-0, Y-Fe-0 and Y-Al-0 are mainly presented. In addition the precipitation-stripping method from organic phase is presented focusing the synthesis of multicomponent powders of Ni-La-0 system. These precipitates have multicomponents homogeneously and so they are converted to multicomponent ceramic powders by calcination. They are important compounds as phosphor, opto-magnetic materials, optical materials, hydrogen storage alloy or as the related precursors. In this presentation some characterization of these particulate materials is included.

Jan 1, 1998

By Takahiro Miki

Soldering material widely used is Sn-Pb alloy, which have low melting point and excellent electrical, strength properties and wettability. However, Pb is one of the toxic elements, which is undesirable due to environmental and safety reasons, thus Pb-free alternative alloy is preferred for new soldering materiaL Sn-Ag and Sn-Zn based alloys have been viewed as very promising candidates, among many potential substitutes. Addition of third element to these alloys will decrease melting point of the alloys. Hence, Sn-Ag-In and Sn-Zn-Mg alloys are expected to be suitable for replacing Sn-Pb solder alloy. In order to dcsign new Pb-free soldering materials, it is crucial to understand precise thermodynamic properties and phase diagrams of alloy systems. In the present work, ion current ratios of Ag to In and Mg to Zn were measured for Sn-Ag-In and Sn-Zn-Mg alloys by mass spectrometry, respectively. Also, the authors reviewed the thermodynamic properties of terminal binary alloys determined by other researchers and evaluated a thermodynamic functions to express the excess Gibbs free energy of each binary alloy. Thermodynamic functions to express the excess Gibbs free energy of liquid Sn-Ag-In and Sn-Zn-Mg ternary alloys were determined, utilizing the assessed Gibbs free energy of terminal binary alloys with the measured ion current ratios using mass speetrometer.

Jan 1, 2003

By Kiyoshi Shibata, Jun-ichi Hayashi

"Steel making technology poses strong potentials for environmental protection in three direction. One is pollution control on steel making process itself. Japanese steel industry has cut down various type of emission drastically since 1970's. Secondary, those process technology can be applied to reduce environmental burden in other industrial sectors. One of the successful examples is municipal waste treatment facility. Thirdly, development of high performance steel products, such as high strength steel for automobile body, can contribute to improve environmental performance during their use, based on the concept of life cycle assessment. Some examples of the successful development and future task is discussed.IntroductionsStack and smoke used to be a symbol of energy intensive industry such as steel making. But, scenery of steel works and its surroundings have been completely changed, and steel products have been changing, as well. The steel making industry consumes huge quantities of energy and resources. Variety of technical development have been carried out to reduce the pollutant release. The steel industry in Japan has been making direct and indirect contributions to reducing of various kinds of environmental impacts through development of high-performance process and products: Its potential technical capability accumulated in steel making is fundamental and essential infrastructure for the vein systems of our society. In this paper, the activity of steel making industry for better environment is discussed"

Jan 1, 2000

By D. D. L. Chung

"In-situ network composites are composites in which the filler network is formed during composite fabrication, in contrast to ex-situ networks which are formed prior to composite fabrication. A homogeneous in-situ network composite has the entire network at the same composition; a heterogeneous in-situ network composite has different parts of the network at different compositions. The homogeneous network composite is made either by the Method of Molten Filler Flow or the Method of Dissolution and Deposition; a heterogeneous network composite is made by the Method of Liquid-Phase Networking. Examples include polymermatrix and metal-matrix composites.IntroductionNetwork composites refer to composites containing a continuous three-dimensional network as the filler. These composites are attractive in their lack of delamination failure, which is usually characterised by two-dimensional composites. The filler and matrix in a network composite can be considered two interpenetrating networks. The mechanical interlocking of the networks adds to the cohesion of the composite. In cases where the filer is much better than the matrix in a certain property, the network nature of the filler makes the filler highly effective in improving that property in the composite in all directions. The property desired in the composite may be high strength, high modulus, low coefficient of thermal expansion, high thermal conductivity, or low electrical resistivity."

Jan 1, 1994

By Dieter Offenthaler

Catalysts used in petroleum industry often contain valuable amounts of PGMs. The typical recycling route for those materials is the pyrometallurgical one, but this treatment way offers limited flexibility with respect to small charge weights. A new process, combining a pyrometallurgical pre-treatment step of the ceramic carriers with a hydrometallurgical leaching procedure overcomes this disadvantage. It not only allows the economical treatment of even very small charge weights, but also gives the possibility to maximize the PGM yield by individually adapting the process to the different charge materials. Due to an ingenious process design, where all leaching agents and effluents are recycled in a closed loop and therefore no waste waters leave the process, process operation becomes very economical. However, the temperature-time-regime in the pyrometallurgical pre-treatment step is of major importance for the success of the whole process. Therefore various investigations have been done to identify how the different process variables in the pyrometallurgical pre-treatment influence the subsequent leaching procedure. It turned out, that the adjustment of the correct phase-modification in the ceramic carrier materials during the pyrometallurgical treatment is the key factor of this process step. Although it is a troublesome issue to exactly adjust the correct phase modifications, it is the prerequisite to take advantage of the benefits of this new process concept.

Jan 1, 2006

By M. I. Kalashnikova

The leaching of metal nickel in copper sulfate solutions is investigated. It is established, that irre-spective of presence or absence of chloride-ion and oxidizer (oxygen) in system process can be divided into three stages, characterizing by restoration and oxidation of metals with formation of metal copper and cuprite and differing in the speeds of sedimentation of copper and transition of nickel into solution. At the initial stage of process along with allocation of metal copper it is be-sieged cuprite, that results in excess of speed of sedimentation of copper in comparison with dis-solution of nickel. At the second stage speed of transition of nickel into solution falls practically to zero, and sedimentation of copper proceeds on reaction of interaction of metal copper with copper sulfate solutions with cuprite formation. During the final period speed of transition of nickel into solution exceeds speed of sedimentation of copper due to course of reaction of resto-ration of cuprite up to metal. Influence of an ion of chloride and oxidizer on formation of various phases is revealed. It is established, that presence of an oxidizer results in increase in a share of cuprite in a deposit. With increase of the maintenance of chloride-ion speed of metal copper allo-cation essentially grows even at presence of an oxidizer in system.

Jan 1, 2006

By Cashman R. S. Mason

Removal of halides (fluoride, chloride) from metallurgical solutions can reduce corrosion rates and improve hygiene from decreased anodic chlorine evolution. This is particularly true for zinc sulphate electrowinning solutions. This paper describes the chemistry of a new process for the removal of halides from such solutions by solvent extraction ? the Teck Cominco Halogon? process, for which patents are pending. In this process, the halides are loaded directly from commercial zinc sulphate solutions and are stripped into a form suitable for disposal. Sulphate extraction efficiency is variable while maintaining halide extraction efficiency. The method of optimizing the solvent composition is demonstrated.

Jan 1, 2003

By Ronald L. Bruening

IBC Advanced Technologies, Inc. (IBC) has developed and commercialized SuperLig® materials based on Molecular Recognition Technology (MRT), which have proven to be very effective for the removal of bismuth from hydrometallurgical sulfuric acid process streams. The most common application is its removal from copper refinery electrolytes, where bismuth control is extremely critical. IBC has also developed an MRT system for extraction, recovery and refining of palladium from a copper refinery by-product stream originating from the treatment of copper tankhouse slimes. A high purity palladium salt is produced which meets market specifications. Results are reviewed and discussed.

Jan 1, 2003

By KNona C. Liddell

"Many metal recovery processes involve heterogeneous reactions in porous media accompanied by fluid flow and mass transfer. Modeling such systems is difficult because of the number of rate processes involved and is complicated even further by effects due to the structure of the porous medium. Data on even bulk properties of the medium are often severely limited or unavailable. For many such systems, a cell model may provide an attractive alternative to models based on transport mechanisms in a differential volume. A cell model requires less input data and is computationally efficient. Identical residence time distributions can be obtained with models of both types, and both allow conversion and concentration profiles and histories to be calculated. The formulation and properties of cell models for metals recovery are described in detail.INTRODUCTIONSubsurface mineral leaching, metal ion recovery and environmental remediation are significant modeling challenges. They involve one-, two-, or three-dimensional reactive flow in multi reaction open systems. Dissolution, adsorption, and ion exchange occur at reactive mineral surfaces, and these heterogeneous reactions are accompanied by acid-base, complexation, and redox reactions in the solution phase.Two approaches have been taken to reactive flow problems in geologic media: mixing cell and transport models. Mixing cell models, the subject of this review, are based on a network of connected cells, each with a specified number of input and output streams. Mixing cells are assumed to have no internal solute concentration gradients, that is, each cell behaves like a well-stirred tank. Gradients are represented by step changes between connected cells; this results in a model that is spatially discretized at the outset. Different methods of discretizing the model equations are considered more fully below. Although this is not strictly necessary, it has usually been assumed in subsurface flow applications that all cells in the network have the same volume and identical initial properties."

Jan 1, 1996

"Injection technology has been an important subject from the early days of ladle metallurgy until the present. During the last decade, there have not been many publications in the area of injection technology. It is the author's opinion that with the challenge to find new solutions especially to environmental and energy related problems as well as better understanding of phenomenas from computer modelling, a new era of inventive injection technology developments is at hand. This is illustrated in the article with examples from six different areas where MEFOS is or have recently carried out R&D work related to issues from the injection technology field. IntroductionThe boom in injection technologies came with the introduction of ladle metallurgy treatment during the '70s and '80s. Since then, the theories and principles have been thoroughly laid down by a number of scientists and also published at several early SCANINJECT conferences.Not many new technologies/applications have been presented during the last ten years. This might lead one to believe that everything is known and done. Those, like MEFOS, who are challenged to find technological solutions to a number of environmental problems and energy saving issues in the pyrometallurgical field are, however, continuously faced with the task of developing new injection technologies.Especially, the call for sustainable technologies to solve environmental problems is a challenge for metallurgists all over the world and it will surely induce a revival of injection technologies. So, in order to encourage all injection experts, let us share some new experiences and let us encourage each other's creativity to solve some of the demands of the future society.The following show some examples of technologies under development, or recently tested."

Jan 1, 1996

By Erwin Flender, Preben N. Hansen, Peter R. Sahm

"Until now FDM-Techniques have been widely used for Modeling Solidification Processes in Castings. Often a rigid, regular type of enmeshment (cubes, , --) have been used. This has the advantage of low CPU-costs, but the disadvantage of a zig-zag presentation of the interface between the casting and the mold. The last point is the reason why FEM-Techniques, giving the possibility of a true presentation of the shape in the enmeshment, are increasingly used. The disadvantage is the high CPU-costs. In this paper, a technique is presented, which uses the FDM-Mesh with the zig-zag presentation of shape and ADI-Algorithms to calculate temperatures and gradients. The new idea is that the calculated parameters are not presented related to the mesh in which they are calculated, but displayed using the true shape of the casting. Such an advantage of both low CPU-costs and shape correct presentation of the calculated results are achieved. IntroductionThe main reason for using a regular type of enmeshment is that it gives the possibility, via ADI-Algorithms, of obtaining a very fast FDM-Technique. The technique presented by P.R. Sahm and P. N. Hansen (1984), and also used by E. Flender (1985), is numerically so stable that average time steps, at least 200 times larger than the limit given by the explicit FDM-Technique, can be applied. To obtain reasonably good results, average time steps in the range of 20 to 50 times the explicit limit seems to be applicable. It should be pointed out,however, that FDM-Techniques can be used on arbitrary nets, the disadvantages being the same as for the FEM-Techniques. This has, among others, been discussed by P.R. Sahm and P.N. Hansen (1984)."

Jan 1, 1986

By Murray Hughes, Neil Brown, John Carran

"A control system architecture has been developed using the Ward-Mellor structured analysis techniques for real-time applications. This approach has produced several advantages over traditional control system implementation methods including:•,partitioning of the control system into discrete control functions.•,easy identification of the interaction between individual control functions and the rest of the system including the impact of changes at the control system boundary (i.e. additional inputs or outputs).•,simplified control software testing.•,a closed loop design, implementation and documentation process.This paper describes a generic control application in which the process specification and control system design are logically linked. Both components are used by process engineers for on-going development.IntroductionAluminium is reduced from alumina in multiple electrochemical semi-batch reactors. Raw material additions and molten metal withdrawal are made at discrete intervals ranging from seconds to days. The electrolytic reduction process is continuous, despite the semi-batch nature of the material inputs and outputs. The chemical and physical processes that occur within each reactor are complex and interdependent, therefore simple methods used for the control of many chemical processes are impractical. The process control system is required to optimise operating efficiencies within the safe operating zone.The process control of aluminium reduction cells is heavily biased towards calculation of process variables with relatively few measured sensors. Each cell is controlled independently of the other cells, although changes to process conditions and raw material . quality will affect all cells. The process responds relatively slowly and with significant time lags. Measurements and process variable calculations occur each second, however the accuracy and precision of actuator response and sensor sampling are measured 111 milliseconds. Time-based scheduling is a significant component of reduction cell control."

Jan 1, 1994

By S. V. Subramanian

The tool material and the machine design for high speed machining are well advanced over the last decade but the steel design has lagged behind. The paper examines the design of steel in order to control the sliding tribology for high speed machining under dry machining conditions. In high speed machining of steel, accelerated chemical wear of the tool occurs once atomic contact is established at the tool-chip interface, resulting in poor tool life even with high performance tools such as cubic boron nitride. Recent research has confirmed the occurrence of nanocrystalline grains in the interfacial layer of the chip at the tool-chip contact. The volume percentage of grain boundary is increased significantly (10 to 30%) as the nanocrystalline grain size is decreased well below 30 nm. The solubility of tool material into the nanocrystalline grain boundary is two or three orders of magnitude greater than in the crystal lattice. Further the kinetics of diffusion in the grain boundary is seven or eight orders of magnitude greater than in the crystal lattice. Enhanced nanocrystalline grain boundary diffusion occurring in the interfacial layer at the tool-chip contact causes the accelerated chemical wear. Significant improvement in tool life could be achieved by engineering glassy oxide inclusions in steel, designed to self-lubricate the tool-chip interface in-situ at higher cutting speeds. Thus the control of sliding tribological condition at the tool-chip interface is key to suppress nanocrystalline layer formation at the tool-chip contact and hence prevent accelerated chemical tool wear. Sulfide inclusions are designed essentially to promote chip fracture. In addition, sulfide inclusions are designed to act as a diffusion barrier at the tool-chip interface. The application of inclusion engineering concepts to enhance the tool life in high speed machining will be demonstrated with a suitable case history.

Jan 1, 2006

By Bruno Lebon, Koulis Pericleous, Georgi Djambazov, Mayur Patel

"High speed compressible jets are used in a number of steel-making applications. In the case of the BOF, a compressible oxygen jet reacts with a carbon-rich iron bath to reduce carbon levels and produce steel. The intensity of the process is governed by the speed of the jet and by the size and shape of the depression created in the metal and slag by the force of the jet, i.e. by the corresponding free surface. This is a difficult CFD problem, since there are compressible and incompressible regions in the flow domain, which need to be handled differently in a finite-volume (FV) pressure-correction scheme. Also, standard turbulence models do not account for compressibility, or the large difference in density between the cold oxygen jet and the hot reacting surroundings. Corrections are introduced to the k-E model to remedy this deficiency and the results are validated against experimental data. The compressible/incompressible boundary is handled through a transition region, based on Mach number.IntroductionThe deformation of a free surface by a compressible high speed jet is of paramount engineering interest, particularly for understanding the physical processes within a Basic Oxygen Furnace (BOF). In a BOF, a supersonic oxygen jet impinges on a molten iron surface, thereby creating a cavity. Oxygen penetrates the bath and removes carbon, resulting in low carbon steel [1].The challenges in modelling such a process lie in coupling a solution domain with distinct compressible and incompressible regions and in dealing with large density differences between the modelled gas and liquid. The modelling of compressibility within the jet is crucial, since the correct velocity profile in the jet is required to determine the cavity depth with accuracy."

Jan 1, 2012

By Cristiän Vargas, Jaime Simpson, Gerardo Cifuentes

"This paper presents a new process for the precipitation of Sb and Bi present in copper refinery electrolytes in the presence of Pb02 (Chilean Patent No. 45,037). To establish the conditions under which the precipitating compounds form, it was necessary to evaluate the amount of PbCh consumed, antimony extraction efficiency, precipitate stability, reaction kinetics, diffraction analysis and X-ray fluorescence, separation of size, plus observation of the precipitates in the electron microscope. Preliminary tests were carried with synthetic copper refinery electrolyte, and then the final testing was done with electrolytes from Chilean refineries. This process provides a real alternative for the treatment of copper refinery electrolytes for the control of Sb and Bi in solution; it is very simple to operate and is low cost compared with competing processes.Introduction.A high quality copper cathode implies a cathode free of impurities. The electrorefining process seeks to eliminate these impurities from the copper anode (99.5% purity) by its dissolution in an acid electrolyte using chemical and electrochemical reactions. As a result of this process, a cathode (99.99% purity) is obtained. If the concentration of impurities in the electrolyte, from the dissolved anodes, begins to increase; particularly if the antimony concentration in the electrolyte increases up 500 ppm, the formation of floating slimes which are a major cause of contamination of the cathode is favoured. The most important impurities from the point of view of their effect on the quality of the cathode copper, are Ag, As, Sb, Bi, Pb, Se and Te. Silver is necessary for the control of Se and Te. To control all of these impurities, it is necessary to establish different methods or parameters of control in copper electrorefining. These parameters are anode composition, additives, purification of the electrolyte, current density, acidity, etc."

Jan 1, 2012

By Krishna Kumar

"Growth of electronics waste (e-waste) and lack of appropriate disposal mechanism are the great concern for developing countries like India. The domestic generation of e-waste in India is rapidly growing with the development. The imported substance is also substantially contributing to the e-waste inventory. Recycling of e-waste is mainly carried out in unorganized units in India. The primitive recycling technique used by the unorganized sector is a great threat to the environment and the health of the operators involved in these profession. Therefore, improvement of technology used by these units towards a cost effective, environmental friendly alternative could be the solution to the present crisis. Few initiatives of recycling have, however, come up in recent years in organized units. The precious metals are still recycled in the developed countries. This report discusses the inventory, technology status, legal legislative and existing practices of e-waste management in India.1. INTRODUCTIONInnovation, research and development in the field of electronics and information and communication technology (ICT) lead to convenient, independent human life. Consumption of electronics and hardware products has enhanced by manifold. Electronics and hardware sectors have, thus, become the fastest growing sector in the world. Faster obsolescence of these products is forcing users to replace products with an advanced technology. Life cycles of these products are few years. Discarded electronics products are, therefore, accumulating alarmingly in our society. Electronics waste (e-waste) is a crisis not only due to its volume but also for presence of its toxic ingredients, like heavy metals (e.g. lead, mercury, cadmium, hexavalent chromium) and flame retardants such as poly brominated biphenyles and poly brominated diphenyles ether. These substances create potential occupational and environmental health hazardous."

Jan 1, 2011

By L. Katgerman, E. N. Straatsma, Suyitno

"Single-roll strip casting process is studied using computational fluid dynamics which takes into account fluid flow, heat transfer and solidification. The computational model is based on the conservation Jaws of momentum, energy and continuity. Correlation of strip thickness, solidification zone length, and puddle shape on single-roll strip casting of Al-1 %Mn is explored. Feeding pressure and roll speed are investigated. The results show that the··strip thickness slightly increases with pressure, similarly the length of solidification zone. The variations of strip thickness and solidification zone length with roll speed show a sharp decline for strip thickness and slight decline for the length of solidification zone with increasing roll speed. The constraint and free-jet flow have different feature in term of flow field. Severe turbulence is observed on the free-jet flow.IntroductionThe near-net shape casting of strip metals is a demand nowadays. The demand is particularly stimulated by the challenge to become more competitive through enhanced performance. The improvement in the existing processes and new innovative technologies are introduced by the metal industry to gain better product quality, more efficiency in energy consumption, low throughput, yield and operating costs [1-3].There are many advantages that can be obtained by the direct casting of strip. The most prominence is the elimination of hot rolling. Beside that the high rate of heat extraction associated with strip casting offers the possibility of a finer, Jess segregated cast structure. The microstructure will result in the improvement of mechanical properties compared to conventional material, or alternatively the opportunity of using grades of metal outside the normal range for continuous casting.The concept of single-roll strip casting has been difficult to commercialize, because of the complex interactions between fluid flow, solidification, shrinkage, and stress, which lead to serious quality problems. Besides that, the quality and the thickness of the strip are affected by the thermal properties of the strip, roll cooling conditions, roll geometry, and other process parameters. To understand how these parameters affect the strip formation, some researchers have modeled the process [4]."

Jan 1, 2004